Steps:
- Determine the number of moles of methane molecules in #11.2 color(white)(l) "L"# of the gas at #"STP"#.
- Calculate the number of moles of #"CO"_2# produced with the stoichiometric relationship in the reaction between methane and excess oxygen.
The IUPAC defines #"STP"# as a set of conditions under which
- Temperature #T=273.15 color(white)(l) "K"#, and
- Pressure #P=10^5 color(white)(l) "Pa"#. [1]
By the ideal gas law
#P * V = n * R * T#
#n=(P * V)/(R * T)#
However, ideal gas constant #R# is typically given in SI units as
#R=8.314 color(white)(l) "N" * "m" * "K"^(-1)#;
Some unit conversions would thus be necessary for the values given in this question.
#1 color(white)(l) "L" = 1 color(white)(l) "dm"^3#
#V=11.2 color(white)(l) "dm"^3=11.2*10^(-3) color(white)(l) "m"^(3)=1.12 xx10^(-2) color(white)(l) "m"^(3)#
#11.2 color(white)(l) "L"# of gas would, thus, correspond to
#n=(10^5 color(white)(l) "N" * color(red)(cancel(color(black)("m"^(-2)))) * 1.12 xx 10^(-2) color(white)(l) color(red)(cancel(color(black)("m"^(3))))) / (8.314 color(white)(l) "N" * color(red)(cancel(color(black)("m"))) * "K"^(-1) * 273.15 color(white)(l) "K")=0.493 color(white)(l) "mol"# of molecules.
Methane combusts in the air to produce carbon dioxide #"CO"_2# and water #"H"_2"O"# when oxygen is in excess. As seen in the balanced equation,
#color(darkgreen)(1) color(white)(l) "CH"_4 (g) + 2 color(white)(l) "O"_2 (g) to color(darkgreen)(1) color(white)(l) "CO"_2 (g) + 2 color(white)(l) "H"_2"O"(g)#,
#(n("CO"_2))=(n("CH"_4))=0.493 color(white)(l) "mol"#.
Note, that some textbooks might assume the IUPAC definition of #"STP"# before the year 1982, where
#P=1 color(white)(l) "atm"= 1.01325 * 10^5 color(white)(l) "Pa"#
is deemed the pressure under standard conditions. See what value would you get for #n("CO"_2)# given #P=1.01325 * 10^5 color(white)(l) "Pa"#.
